A Novel Binary Particle Swarm Optimization

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A Novel Binary Particle Swarm Optimization
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Binary PSO- One version

• In this version of PSO, each solution in the
  population is a binary string.
• Each binary string is of dimension n which is
  evaluated to give parameter values.
• In the binary PSO, each binary string represents
  a particle
• Strings are updated bit-by-bit based on its
  current value, the value of that bit in the best
  (fitness) of that particle to date, and the best
  value of that bit to date of its neighbors

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Binary PSO- What is a neighbor?

• For binary strings, neighbors can be selected in
  one of several ways. Some examples are (for a
  neighborhood of size k)
• Neighbors are the k binary strings whose Hamming
  distance is minimum
• For equal Hamming distances, the choices are
  arbitrary
• In the beginning, arbitrarily assign groups of k
  strings to neighborhoods
• Let the neighborhood size be the population size

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BPSO

• In regular (real valued) PSO, everything is in
  terms of a velocity.
• In BPSO, how does one define a velocity for a
  single bit?
• Generally the velocity is defined in terms of a
  probability of the bit changing
• You will see in a minute how this works

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BPSO

• As just noted, in BPSO, bit-by-bit updates are
  done probabilistically
• In other words, for a chosen bit (d) in a chosen
  string (i) it is changed to a 1 with a
  probability (P) that is a function of its
  predisposition to be a 1, the best value of
  itself to date, and the best value of its
  neighbors.
• 1-P is the probability of changing to a 0
• Once P is determined, we generate a random number
  R, and if RltP, then the bit becomes a 1
  otherwise it becomes a 0

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BPSO

• The formula for an individual bits update is
• The function P is a probability, and thus once
  this value is computed for a given particle bit,
  we must generate a uniform random number to see
  whether it should be a 1 or a 0

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BPSO
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BPSO

• The challenge is to come up with the f() from the
  previous slide
• The value of vid(t) determines a strings
  propensity to choose 1 or 0.
• Higher values of vid(t) mean it is more likely to
  choose a 1, similarly for lower values choosing a
  0

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BPSO

• For the function
• We are saying that this probability is a function
  of the bits current value, its velocity and
  the values of the best to date for the bit and
  best to date for the neighborhood.
• Remember, best to date for a bit is simply a 0 or
  a 1

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BPSO

• Since f will be a probability value, we know it
  must range between 0 and 1.
• There are several measures or expressions used
  for f, one that is commonly used is the sigmoid
  function

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BPSO

• In the preceding
• Sometimes these parameters are chosen from a
  uniform distribution 0 - 2, such that the sum of
  their two limits is 4.0

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BPSO Example

• As an example, lets say that we are dealing with
  a population of 5 bit binary particles and a
  population of 4 particles
• 10101
• 01011
• 11100
• 01101
• We are updating particle 2 (01011), bit 3 (0)

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BPSO Example

• Furthermore, we will assume that the current
  propensity (velocity) of this bit to be a 1 is
  0.25.
• Furthermore, assume that the best value of this
  particle (to date) was 00100
• And the best value of the whole population (to
  date) was 01111

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BPSO Example

• Thus we have

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BPSO Example

• Now, with the value for f, we generate a random
  number, and if it is lt f then bit x becomes a 1
  otherwise, it becomes a 0.

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BPSO - Parameters

• Sometimes the v value is limited so that f does
  not approach too closely to 0.0 or 1.0.
• In this case, constant parameters Vmin ,Vmax is
  used.
• When vid is gt Vmax, vid is set to Vmax
• When vid is lt Vmin, vid is set to Vmin

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BPSO - Initializing

• There are a few things that need to be
  initialized.
• Initial population (particle) values just
  randomly generate binary strings
• Initial velocities can be generated as

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Main problems with binary PSO

• Parameters of the binary PSO
• the effects of these parameters are the opposite
  of those for the real valued PSO
• values ofw lt 1 prevents convergence. For values
  of -1ltw lt1,Vij becomes 0 over time. for w lt 1 we
  have
• Memory of BPSO

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Proposed Binary Particle Swarm Optimization

• Two velocities for PSO

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Results
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